I am not sure what kind of potty to begin with for a girl. I have started looking around and I am not sure if we need one with a back, with a liftable seat, one that attaches to our toilet, one with cartoon characters on it or the basic $3 model from Ikea, etc. Can anyone recomend where to start?

With My kids I made a big deal about it tell them they are big kids now and let them pick out their own " BIG KID Potty" that way they felt big and some kinda of owner ship in their Potty.

That being said I gave them 3 choices to pick from. this is what I did Small potty that sat on floor with a back ( Cause it looks more like mommy potty, and they did not have to climb up a step to get to it.)
No lid ( the kids already has to deal with their pants why make more work for them)
The little potty I got the tops could come off and transition with my kids to the full size Potty because fit in the lid, to help with their confidence that they would not fall in.
Hope this helps

I agree with Mary about giving the child the chance to choose, we were a bit cheeky in that we had already narrowed down our own choice, we just offered our daughter to pick the colour she wanted :)

We went for a style that was comfortable to sit in, I had heard from friends who were more experienced mothers that comfort was a big issue, particularly during the early stages when you have to encourage them to actually enjoy sitting on the potty. So this was something we were conscious about.

Also we wanted a style that was easy to clean, hold, and wash. So we only considered the potties with the removable pans.

We used the Babybjorn Potty Chair model and would recommend it without any hesitation. I can also tell you that my motherinlaw had the regular potty model from Ikea, at her house, my daughter did use it when we were there.